I love origami, and it recently gave me an idea for a very hard but beautiful puzzle. I'm really curious whether anyone here can solve it.
So here's the puzzle. You are given a large perfectly square piece of paper with no marks on it. With this square, you have to make a square of exactly one-fifth the area of the original square. You are given no tools such as a ruler or scissors, and all you can do is fold the paper. How do you solve this?